Three-vs. four-point bending test for the characterization of plain concrete: a numerical investigation

In this paper the Three-Point-Bend (3PB) and the Four-Point Bend (4PB) tests are extensively examined with reference to plain concrete. The investigation is based on several numerical analyses performed using a non-local damage model already successfully employed in reproducing mode I fracture process in concrete. The need for this research arose in the framework of UNI and RILEM Technical Commissions devoted to select a test suitable for the characterization of mechanical properties in tension of Steel Fiber Reinforced Concrete (SFRC). The test has to emphasize the fiber contribution in mode I fracture behavior with respect to that offered by the same plain concrete matrix. Different reasons moved the Commissions to consider as standard bending test two different notched specimen geometries, furthermore characterized by two different notch depths. The Italian Committee (UNI) chose the 4PB and the International Committee (RILEM) decided for the 3PB. The final purpose of this work is hence to compare these two bending test-geometries with reference to peak load, energy-release contributions, crack-tip and mouth opening displacements, deflections, regarding as variables the notch depth, the load position, the specimen size and the concrete class. The influence of defects was not taken into account, because only the choice of the specimen geometry was debated. It has been found that the values of both Crack Tip Opening Displacements (CTOD) and deflections at the peak load are almost independent of specimen geometry and testing variables and are weakly dependent on concrete strength. A semi-empirical relationship between crack-opening displacement and deflection is also proposed in order to simplify as much as possible the test set-up.